Decidability and undecidability of extensions of second (first) order theory of (generalized) successor
Keyword(s):
We study certain first and second order theories which are semantically defined as the sets of all sentences true in certain given structures. Let be a structure where A is a non-empty set, λ is an ordinal, and Pα is an n(α)-ary relation or function4 on A. With we associate a language L appropriate for which may be a first or higher order calculus. L has an n(α)-place predicate or function constant P for each α < λ. We shall study three types of languages: (1) first-order calculi with equality; (2) second-order monadic calculi which contain monadic predicate (set) variables ranging over subsets of A; (3) restricted (weak) second-order calculi which contain monadic predicate variables ranging over finite subsets of A.
1996 ◽
Vol 307
◽
pp. 135-165
◽
Keyword(s):
1984 ◽
Vol 51
(4)
◽
pp. 745-752
◽
1974 ◽
Vol 32
◽
pp. 400-401
Keyword(s):
Keyword(s):
2001 ◽
Vol 11
(1)
◽
pp. 21-45
◽
Keyword(s):
Keyword(s):
Keyword(s):
Keyword(s):